The procedure is still highly experimental, and not all of the risks are known. Here's what you need to know about uterus transplants:

Who needs a uterus transplant?

The new study will involve women with a condition called uterine factor infertility, which means they cannot become pregnant either because they were born without a uterus, or their uterus was removed by hysterectomy, or it was damaged by an injury or infection so that it no longer functions, according to the Cleveland Clinic.

Women ages 21 to 45 are eligible for the study, but those 40 and older must have undergone fertility treatments to create and freeze embryos before they were 39, the Clinic says.

About 1 in 4,500 women in the United States is born without a uterus - a condition known as Mayer-Rokitansky-Küster-Hauser syndrome, according to the NIH.

However, unlike the study in Sweden, in which patients received uteruses that were donated by living relatives, the study at the Cleveland Clinic will use deceased donors. Using organs from deceased donors avoids having a living donor take on the risks of uterine removal surgery. Injuries can occur when surgeons try to remove blood vessels that surround the organ, according to the New York Times.

Because of the tricky work that is needed to avoid cutting blood vessels, an operation on a live donor takes between seven to 11 hours, the Times said. The uterus can be removed from a deceased donor much faster.

Researchers in the United Kingdom also plan to perform a similar trial of uterus transplants using deceased donors next year. However, the researchers need to raise $756,300 (£500,000) before they can being their study.

Will the women be able to become pregnant from sex?

No, women who receive the uterus transplants will not be able to become pregnant without fertility treatments, because the transplanted uterus will not be connected to their fallopian tubes, where normal fertilization takes place.

Instead, the women will need to undergo in vitro fertilization, in which eggs are removed from their ovaries and fertilized in a lab dish, and implanted in the uterus. The doctors who are conducting the study will not begin the search for a uterus donor for a woman until she has undergone IVF, and has frozen embryos.

If all goes well and the women become pregnant, they will need to have a cesarean section, so that the transplanted uterus will not go through the trauma of labor, the Times said.

What are the risks?

The women who receive the transplants will need to undergo a major surgery, which is always risky. These risks factor into the ethics of doing the surgery — some have argued that, because transplant surgeries have such high risks, and this one is not life-saving, it is not ethical to perform.

However, others argue that the procedure is ethical because it could so dramatically improve a woman's quality of life. "Being able to carry a pregnancy and have a biological child, that’s extremely important" to some women, Lisa Campo-Engelstein, an assistant professor at the Center for Biomedical Ethics Education and Research at Albany Medical College in New York, told Live Science in an interview last month. She also noted that much of today's medicine is focused on improving people's quality of life.

The women who receive a uterus transplant will also need to take immunosuppressant drugs so that their body does not reject the organ, and it's not exactly clear how these drugs may affect a developing fetus. These drugs have side effects, including an increased risk of infection, and they may increase the risk of preterm delivery.

However, studies done on women who have undergone kidney transplants and later become pregnant have found that immunosuppressant drugs are relatively safe in pregnancy.

The new study will also have unknown risks, compared to the Swedish study, because it will use organs from deceased donors. Organs from deceased donors could be slightly compromised because of the decline in the donor's health that happens before death, Arthur Caplan, director of the Division of Medical Ethics at New York University's Langone Medical Center, told Live Science in an interview last month.

After the transplant, how long will it be before the women become pregnant?

The women must wait a year following the transplant before the embryos can be implanted, the Cleveland Clinic says. This gives the uterus time to heal.

What happens after the women give birth?

After a successful birth, the women will have the option to keep the transplanted uterus and try to have another baby. But after two babies, the women will need to have a hysterectomy to remove the uterus so that they can stop taking immunosuppressant drugs, which carry long-term risks, the Clinic says.